A honeycomb structure is widely used as a filter that purifies an exhausted gas from an internal combustion engine, such as a diesel particulate filter (see Patent Literature 1, for example). Since soot removed from an exhaust gas build up in the honeycomb structure, filter regeneration in which the soot is burned is required every fixed period. To burn soot, a large amount of hot combusted exhaust gas may be supplied to ignite the soot and burn it completely.